This invention relates to optical fiber waveguides and more particularly to optical fiber waveguides wherein two dopants are radially graded in a silica based fiber for the purpose of achieving minimum modal dispersion over a broader range of wavelengths than is possible with only one dopant.
It has been known in the prior art that modal dispersion in a multimode optical fiber can be minimized by radially grading the refractive index in the core of the fiber, see the article entitled "Light Propagation in Generalized Lens-Like Media" By S. E. Miller Bell System Technical Journal, Vol. 44, page 2017, 1965. To achieve this minimum modal dispersion it has been established that the refractive index should be graded in accordance with the following equation: EQU n(r) = n.sub.c (1 + f(r))
where n(r) is the index at radius r from the axis and n.sub.c is the refractive index at the core-cladding interface. The function f(r) has a form provided by the following equation: ##EQU1## WHERE .DELTA. IS THE RELATIVE INDEX DIFFERENCE GIVEN IN TERMS OF THE FOLLOWING EQUATION: ##EQU2## IN WHICH N(0) IS THE REFRACTIVE INDEX VALUE AT R = 0, AND .alpha. IS AN EXPONENT THAT WAS FOUND TO DEVIATE FROM 2 BY A TERM IN THE ORDER OF .DELTA. IN ORDER TO PROVIDE MINIMUM MODAL DISPERSION. This value of the exponent was described by D. C. Gloge and E. A. J. Marcatili in their U.S. Pat. No. 3,823,997 issued July 16, 1974.
It was subsequently determined that the dispersion of the index of refraction should be taken into account in order to achieve minimum modal dispersion. Under these circumstances it was determined that the shape of the index profile still follows a near parabolic shape but the exponent .alpha. was determined to deviate from 2 by an amount 2P which may be substantially larger than the relative index difference .DELTA.. This determination is set forth by D. B. Keck and R. Olshansky in their U.S. Pat. No. 3,904,268 issued Sept. 9, 1975. Their precise expression for the optimum .alpha. is as follows: ##EQU3## The magnitude of the contribution of the third term having .DELTA. as a coefficient is determined to be small (in the order of 0.01) and this term may therefore be ignored since it is difficult to take into account experimentally at the present time. Hence, the optimum .alpha. for minimum modal dispersion is approximately equal to (2-2P) where the profile dispersion P is defined by the following equation: ##EQU4## Inasmuch as the group index N deviates from n by less than 1 percent it can also be assumed that N equals n and the profile dispersion may be expressed in terms of the following equation: ##EQU5##
The refractive index profile is generally achieved in a multimode fiber by varying the concentration of an added dopant as a function of radius r. See for example, the U.S. Pat. No. 4,033,667 entitled "Multimode Optical Fiber" issued July 5, 1977 to J. W. Fleming wherein it is proposed that phosphorus pentoxide and boron oxide be added to a silica based fiber in order to achieve minimum modal dispersion at a single wavelength and increased numerical aperture.
In U.S. Pat. No. 4,025,156 entitled "Graded Index Fiber for Multimode Optical Communications" by D. C. Gloge et al, issued May 24, 1977 germanium dioxide and boron oxide are radially graded in the core of a multimode fiber in order to achieve minimum modal dispersion over a broad range of wavelengths. These two dopants germanium dioxide and boron oxide when properly graded in a single fiber produce a fiber whose optimum .alpha. versus wavelength curve has substantially zero slope over a broad range of wavelengths. As a result, a fiber of this type can be installed for use at one wavelength and later used at a much different wavelength without introducing any loss due to modal dispersion. Unfortunately, boron oxide may have an unpredictable effect on the refractive index of the host glass even in small concentrations. As a result, the addition of boron oxide produces a reduction in the refractive index that can vary nonlinearly with concentration and can also vary strongly with the thermal history of the glass. Hence, boron oxide is not as predictable in its behavior as one would like in order to design fibers having reproducible performance in their qualities of modal dispersion.